Mesoscopic Josephson effect in graphene disk at magnetic field

Unlike for tunneling Josephson junctions, for which the current-phase relation is given by the sine function, with the critical current ($I_c$) and normal-state resistance ($R_N$) following the relation $I_c{R}_N=(\pi \mathrm{/}2){\mathrm{\Delta }}_0\mathrm{/}e$ (where ${\mathrm{\Delta }}_0$ is the superconducting gap and electron charge is $-e$), mesoscopic Josephson junctions show more complex current-phase relations, with the skewness $S>0$, what is related to the presence – in case the leads are in the normal state – of transmission probabilities taking the values comparable to $1$. Here, we show that these features also appear for a superconductor-graphene-superconductor (S-g-S) junction in the disk-shaped (Corbino) geometry, when the magnetic field is adjusted such that $I_c\to 0$ and $R_N\to \mathrm{\infty }$. In such a case, the product $I_c{R}_N\approx 1.85{\mathrm{\Delta }}_0\mathrm{/}e$, and the skewness $S\approx 0.14$. The results obtained from quantum-mechanical mode-matching analysis for the Dirac-Bogoliubov-De-Gennes equation are compared with simpler model assuming incoherent scattering between two circular interfaces separating the sample and the leads.